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Let $V$ be an inner product space. What is the value of $^2 = $?

where $u, v \in V$ and $<,>$ is the inner product on $V$.

Thanks for your help.

  • 0
    Are you asking what the definition of $\langle u,v\rangle$ is? – 2017-02-04
  • 1
    $\langle u,v \rangle ^2 = \langle u,v \rangle \, \langle u,v \rangle\,$. Did you mean to ask something else maybe? – 2017-02-04
  • 1
    It depends on what $u$ and $v$ are. Generically, $^2=(u_1v_1+\dots+u_nv_n)^2$, and you can develop the square of the sum. – 2017-02-04

1 Answers 1

2

If $\alpha$ is the angle between $u$ and $v$ then

$^2=||u||^2*||v||^2*\cos^2(\alpha)$

  • 0
    Ooops, of course, angle ! – 2017-02-04